Neter J., Kutner M.H., Wasserman W. — Applied Linear Regression Models :: Электронная библиотека попечительского совета мехмата МГУ

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Neter J., Kutner M.H., Wasserman W. — Applied Linear Regression Models

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Название: Applied Linear Regression Models

Авторы: Neter J., Kutner M.H., Wasserman W.

Аннотация:

Applied Linear Regression Models was listed in the newsletter of the Decision Sciences Institute as a classic in its field and a text that should be on every member's shelf. The third edition continues this tradition. It is a successful blend of theory and application. The authors have taken an applied approach, and emphasize understanding concepts; this text demonstrates their approach trough worked-out examples. Sufficient theory is provided so that applications of regression analysis can be carried out with understanding. John Neter is past president of the Decision Science Institute, and Michael Kutner is a top statistician in the health and life sciences area. Applied Linear Regression Models should be sold into the one-term course that focuses on regression models and applications. This is likely to be required for undergraduate and graduate students majoring in allied health, business, economics, and life sciences.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1983

Количество страниц: 720

Добавлена в каталог: 27.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

"Best" subsets algorithms      429
$C_{p}$ criterion      426—428
$MSE_{p}$ criterion      423—425
$R^{2}_{a}$ criterion      423—425
$R^{2}_{p}$ criterion      422—423
Addition theorem      2
Adjusted coefficient of multiple determination      241—242
All-possible-regressions selection procedure      421—429
Allocated codes      351—352
Analysis of variance      84—86
Analysis of variance models      343
Analysis of variance table      89—90
ANOVA table      89—90
Asymptotic normality      70
Autocorrelation      444—448
Autocorrelation parameter      448
Autocorrelation, remedial measures      454—460
Autocorrelation, test for      450—454
Autoregressive error model      see "Regression model"
Backward elimination selection procedure      435—436
Berkson model      166—167
Beta coefficient      262
Biased estimation      394—395
Binary variable      330 354 see
Bivariate normal distribution      492—496
BMDP      113 251 431
Bonferroni joint estimation procedure for inverse predictions      174
Bonferroni joint estimation procedure for mean responses      158—159 245
Bonferroni joint estimation procedure for prediction of new observations      159—160 246—247
Bonferroni joint estimation procedure for regression coefficients      150—154 243
Calibration problem      174
Central limit theorem      6
Chi-square distribution      7—8
Chi-square distribution, table of percentiles      520
Cochran's theorem      92
Coefficient of multiple correlation      242 506
Coefficient of multiple correlation, inferences      506—507
Coefficient of multiple determination      241 506
Coefficient of multiple determination, adjusted      241—242
Coefficient of multiple determination, inferences      506—507
Coefficient of partial correlation      288—289 507—508
Coefficient of partial correlation, first-order      508
Coefficient of partial correlation, inferences      508
Coefficient of partial correlation, second-order      508
Coefficient of partial determination      286—288 507—508
Coefficient of partial determination, inferences      508
Coefficient of simple correlation      97—99 494
Coefficient of simple correlation, inferences      502—504
Coefficient of simple determination      96—97 501—502
Coefficient of simple determination, inferences      502—504
Column vector      187
Complementary event      3
Conditional probability      3
Conditional probability function      4
Confidence coefficient, interpretation of      70—71 84
Confidence set      152
Consistent estimator      9
Contour diagram      235—237 494—495
Cook's distance measure      407—409
Correction for mean sum of squares      90
Correlation coefficient      see "Coefficient of multiple correlation" "Coefficient "Coefficient
Correlation Index      312
Correlation matrix      382
Correlation matrix of the independent variables      381
Correlation model      491—492
Correlation model, bivariate normal      492—496
Correlation model, multivariate normal      505
Correlation transformation      378—379
Covariance models      343
Covariance of two functions of random variables      6
Covariance of two random variables      5
Cox, D.R.      176
Degrees of freedom      7—8
Deleted residual      405—406
Denominator degrees of freedom      8
Dependent variable      25 28
Determinant of matrix      202
Diagonal matrix      196—197
Disturbance term      445
Dummy variable      34 330 see
Durbin — Watson test      450—454
Durbin — Watson test, table of test bounds      530—531
Error mean square      47
Error sum of squares      47
Error term      31
Error term variance      31 46—48 50
Error term, nonconstancy of error variance      113—114 123 133
Error term, nonindependence of      116—118 123 133
Error term, nonnormality of      118—120 123 133
Expected mean square      90—91
Expected value of function of random variables      5—6
Expected value of random variable      3
Experimental data      35
Exponential regression function      468
Extra sum of squares      282—286
F distribution      8—9
F distribution, table of percentiles      521—527
Family confidence coefficient      150
Family of estimates      150
First differences      458—459
First-order autoregressive error model      448—450
First-order autoregressive error model, first differences approach      458—460
First-order autoregressive error model, iterative estimation approach      455—458
First-order autoregressive error model, test for autocorrelation      450—454
First-order regression model      31 227 229—230 see
Fisher, R.A.      503
Fitted value      41
Fitted value in terms of hat matrix      401
Forward selection procedure      435
Full model      95
Functional relation      24
Gauss — Markov theorem      39—40 64
Gauss — Newton method      472—479
General linear regression model      230—234 237—238
General linear test      94—96 293—296
Hat matrix      220—221
Heteroscedasticity      170
Homoscedasticity      170
Hyperplane      230
Idempotent matrix      221
Identity matrix      197
Independence of random variables      5
Independent variable      25 28
Indicator variable      329—330 353—354
Indicator variable in comparing regression functions      343—345
Indicator variable in piecewise linear regression      346—350
Indicator variable in time series model      350—351
Indicator variable, as dependent variable      354—357
Influential observations      407—409
Instrumental variable      165—166
Interaction effect      232—237
Interaction effect coefficient      304
Interaction effect with indicator variables      335—339
Intrinsically linear regression model      467
Inverse of matrix      200—204
Inverse prediction      172—174
Joint confidence region for regression coefficients      147—150 217 243
Joint probability function      4
Lack of fit mean square      129
Lack of fit sum of squares      128
Lack of fit test      123—132 245—246
Least absolute deviations estimation      410—411
Least squares criterion      36
Least squares estimation      10
Least squares estimation, control of roundoff errors      377—382
Least squares estimation, multiple regression      238—239
Least squares estimation, nonlinear regression      470—480
Least squares estimation, simple linear regression      36—40 44—46 210—212
Least squares estimation, weighted      167—172 219—220 263
Leverage      402

Likelihood function      9
Linear dependence      199—200
Linear effect coefficient      301
Linear model      31 466—467 see
Linear model, general linear test      94—96 293—296
Linear regression model      see "Regression model"
Linearity, test for      123—132
Logistic regression function      361—362 468—469
Logistic transformation      362
Logit transformation      362
Marginal probability function      4
Marquardt algorithm      479—80
Matrix of quadratic form      215
Matrix with all elements      1 198
Matrix, addition      190—191
Matrix, definition      185—187
Matrix, determinant      202
Matrix, diagonal      196—197
Matrix, dimension      186
Matrix, elements      186
Matrix, equality of two      189
Matrix, hat      220—221
Matrix, idempotent      221
Matrix, identity      197
Matrix, inverse      200—204
Matrix, multiplication by matrix      192—196
Matrix, multiplication by scalar      192
Matrix, nonsingular      201
Matrix, random      205—208
Matrix, rank      200
Matrix, scalar      197—198
Matrix, singular      201
Matrix, square      187
Matrix, subtraction      190—191
Matrix, symmetric      196
Matrix, theorems      204—205
Matrix, transpose      188—189
Matrix, vector      187—188
Matrix, zero vector      198—199
Maximum Likelihood Estimation      9—10
Maximum likelihood estimation of regression parameters      50—51
Mean of population, estimation of difference between two      14—16
Mean of population, estimation of single      11
Mean of population, test concerning, difference between two      14—16
Mean of population, test concerning, single      11—12
Mean response      41
Mean response, multiple regression, estimation      244
Mean response, multiple regression, joint estimation      245
Mean response, simple linear regression, interval estimation      75—76 217
Mean response, simple linear regression, joint estimation      157—159
Mean response, simple linear regression, point estimation      41—43
Mean square      46 88
Mean square, expected value of      90—91
Mean squared error of regression coefficient      395
Mean squared error, total of n fitted values      426
Measurement errors in observations      164—167
Method of steepest descent      479
Minimum absolute deviations method      411
Minimum sum of absolute deviations method      411
Minimum variance estimator      9
Minimum- $L_{1}$ -norm method      411
Multicollinearity      271—278 382—390
Multicollinearity, detection of      390—393
Multicollinearity, remedial measures      393—400
Multiple correlation      see "Coefficient of multiple correlation"
Multiple regression      see "Mean response" "Prediction "Regression "Regression "Regression "Selection
Multiplication theorem      3
Multivariate normal distribution      505
Noncentrality parameter      71
Nonexperimental data      35
Nonlinear regression model      468—469
Nonlinear regression model, inferences about parameters      480—483
Nonlinear regression model, least squares estimation      470—480
Nonsingular matrix      201
Normal equations      38
Normal error regression model      see "Regression model"
Normal probability distribution      6—7
Normal probability distribution, table of areas and percentiles      517
Normal probability plot      118—120
Numerator degrees of freedom      8
Observation      25
Observational data      35
Observed value      41
Orthogonal polynomials      319
Outlier      114—116 123
Outlier, identification of      400—407
Overall F test      281 289
p-value      12—13
Paired observations      15—16
Partial correlation      see "Coefficient of partial correlation"
Partial F test      281 289
Partial regression coefficient      229
Piecewise linear regression      346—350
Point estimator      38
Polynomial regression model      300—305
Power of tests for regression coefficients      71—72
Prediction bias      437
Prediction interval      77—78
Prediction of new observation, inverse      172—174
Prediction of new observation, multiple regression      246—247
Prediction of new observation, simple linear regression      76—82 159—160 218—219
Predictor variable      25 28
Probit transformation      366
Product operator      2
Pure error mean square      127—128
Pure error sum of squares      127
Quadratic effect coefficient      301
Quadratic form      215
Quadratic response function      301
Quadratic response function, estimation of maximum or minimum      317—319
Quantal response      354
random matrix      205—208
Random vector      205—208
Rank of matrix      200
Reduced model      95
Regression      see "Mean response" "Prediction "Regression "Regression "Regression
Regression coefficients, multiple regression      227—229
Regression coefficients, multiple regression, danger in simultaneous tests      278—282
Regression coefficients, multiple regression, interval estimation      243
Regression coefficients, multiple regression, joint estimation      243
Regression coefficients, multiple regression, point estimation      238—239 263
Regression coefficients, multiple regression, tests concerning      243 285—286 289—293
Regression coefficients, multiple regression, variance-covariance matrix of      242 263
Regression coefficients, partial      229
Regression coefficients, simple linear regression      33—34
Regression coefficients, simple linear regression, interval estimation      65—67 69—70
Regression coefficients, simple linear regression, joint estimation      147—154 217
Regression coefficients, simple linear regression, point estimation      36—40 50—51 167—172 210—212 219—220
Regression coefficients, simple linear regression, tests concerning      67—68 71—72 92—94
Regression coefficients, simple linear regression, variance-covariance matrix of      216—217
Regression coefficients, standardized      261—263
Regression curve      27—28 see
Regression function      27—28
Regression function, comparison of two or more      343—45
Regression function, confidence band, simple linear regression      154—157
Regression function, confidence region, multiple regression      244
Regression function, estimated regression function      41—43
Regression function, test for fit      123—132 245—246
Regression function, test for regression relation      92—93 240—241
Regression function, transformations to linearize      134—141
Regression mean square      88
Regression model      26—29
Regression model, effect of measurement errors      164—167
Regression model, first-order autoregressive      448—450
Regression model, general linear      230—234 237—238
Regression model, multiple      226—230
Regression model, multiple in matrix terms      237—238
Regression model, multiple with interaction effects      232—237 335—339
Regression model, nonlinear      468—469
Regression model, polynomial      300—305

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